PIMS/CSC Distinguished Speaker Series: Yanghong Huang

Abstract:

We consider the aggregation equation \rho_t =
\nabla\cdot(\rho \nabla K*\rho) in R^n, where the interaction potential K models short-range singular repulsion and long-range power-law attraction. Here, \rho represents the density of the aggregation and K is a social interaction kernel that models attraction and repulsion between individuals. We show that there exist unique radially symmetric equilibria supported on a ball. We perform asymptotic studies for the limiting cases when the exponent of the power-law attraction approaches infinity and a Newtonian singularity, respectively. Numerical simulations suggest that equilibria studied here are global attractors for the dynamics of the aggregation model. This work is in collaboration with Razvan Fetecau (SFU) and Theodore Kolokolnikov (Dalhousie).